The matrix diagram shows the relationship between two, three or four groups of information. Depending on the type of matrix, it may illustrate supporting information about the relationship, such as the relationship strength, the roles played by various individuals or measurements. Here we discuss six differently shaped matrices, L, T, Y, X, C and roofshaped
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Table 1 summarizes when to use each type of matrix diagram. In the below examples, we shaded the matrix axes to emphasize the letter that gives each matrix its name. You chose the matrix that matches the number of groups and interested interactions.
An Lshaped matrix relates two groups of items to each other (or one group to itself).
A Tshaped matrix diagram relates three groups of items: groups B and C are each related to A. Groups B and C are not related to each other.
A Yshaped matrix relates three groups of items. Each group is related to the other two.
A Cshaped matrix simultaneously relates three groups of items at one 3D point.
An Xshaped matrix relates four groups of items. Each group is related to two others.
A roofshaped matrix relates one group of items to itself. It can be used by itself or as a roof to a L or Tshaped matrix.
This Lshaped matrix summarizes customers' requirements. The team placed numbers in the boxes to show numerical specifications and used check marks to show choice of packaging.
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The Lshaped matrix actually forms an upsidedown L. This is the most basic and most common matrix format.
This Tshaped matrix relates product models (group A) to their manufacturing locations (group B) and to their customers (group C). Examining the matrix in different ways reveals different information.
For example, concentrating on model A, we see the Texas plant produces it in a large volume and the Alabama plant manufactures a small volume. Time Inc. is the major customer for Model A, while Arlo Co. buys a small amount.
If we choose to focus on the customer rows, we learn only one customer, Arlo, buys all four models. Zig buys just one. Time makes large purchases of A and D, while Lyle is a relatively minor customer.
This Yshaped matrix shows the relationships between customer requirements, internal process metrics and the departments involved. Modified symbols show the strength of the relationships:
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The matrix tells an interesting story about ontime delivery. The company assigned the distribution department primary responsibility for the ontime requirement. Two metrics that most strongly relate to ontime delivery are inventory levels and order lead time. Of the two, distribution has only a weak relationship with order lead time and none with the inventory levels. Perhaps the responsibility for ontime delivery needs to be reconsidered. Based on the matrix, where would you put responsibility for ontime delivery?
Think of C meaning cube.Because this matrix diagram is threedimensional, it is difficult to draw and infrequently used.
If it is important to compare three groups simultaneously, consider using a threedimensional model or computer software that can provide a clear visual image.
This figure shows one point on a Cshaped matrix relating products, customers and manufacturing locations. Zig Company's model B is made at the Mississippi plant.
This figure extends the Tshaped matrix example into an Xshaped matrix by including the relationships of freight lines with the manufacturing sites they serve and the customers who use them.
Each axis of the matrix is related to the two adjacent ones, but not to the one across. Thus, the product models are related to the plant sites and to the customers, but not to the freight lines.
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A lot of information can be contained in an Xshaped matrix diagram. In this one, we observe that Red Lines and Zip Inc., which seem to be minor carriers based on volume, are the only carriers that serve Lyle Co. Lyle doesn't buy much, but it and Arlo are the only customers for model C. Model D is made at three locations, while the other models are made at two. What other observations can you make?
The roofshaped matrix is used with an L or Tshaped matrix to show one group of items relating to itself. It is most commonly used with the house of quality, where it forms the roof of the house.
In the figure below, the customer requirements are related to one another. For example, a strong relationship links color and trace metals, while viscosity is unrelated to any of the other requirements.
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